A poor installation will result in higher cpu temperatures.
To mount the Intel stock cooler properly, place the motherboard on top of the foam or cardboard backing that was packed with the motherboard.
The stock cooler will come with paste pre applied, it looks like three grey strips.
The 4 push pins should come in the proper position for installation, that is with the pins rotated in the direction of the arrow,(counter clockwise) as far as they can go.
If you want, play with the pushpin mechanism until you know how they work.
Place the cooler so that all 4 pins are oriented over the holes in the motherboard.
Push down on the entire cooler so that all 4 pins are through the motherboard.
When you push down on the top black pins, it expands the white plastic pins to fix the cooler in place.
The trick to getting it on is to push down on a DIAGONAL pair of pins at the same time. Then the other pair.
If you push them in one at a time, you will not get the cooler on straight.
Lastly, look at the back of the motherboard to verify that all 4 pins are equally through the motherboard, and that the cooler is on firmly.
This last step must be done, which is why the motherboard must be out of the case to do the job.
It is possible to mount the cooler with the motherboard mounted in the case, but you can then never be certain that the push pins are inserted properly.
If you should need to remove the cooler, turn the pins clockwise to unlock them.
You will need to clean off the old paste and reapply new if you ever take the cooler off.